How do I Simplify This Integral: 9r4^r dr?

  • Thread starter Joy09
  • Start date
  • Tags
    Integral
In summary, to evaluate the integral of 9r4^r dr, you can use the formula integral of f(x)g'(x)dx = f(x)g(x) - integral of f'(x)g(x)dx and set u=r, du=dr, dv=4^r, v=(4^r)/ln(4). This results in the equation [(r4^r)/ln4] - 1/ln4[the inegral of 4^r dr]. Simplifying this by multiplying 9 through and adding +C at the end, you get the final solution of 9[(r4^r)/ln4] - 9/ln4[(1/ln(
  • #1
Joy09
2
0

Homework Statement



Evaluate the integral:
the integral of 9r4^r dr


Homework Equations



integral of f(x)g'(x)dx = f(x)g(x) - integral of f'(x)g(x)dx

integral of udv = uv - integral vdu

u = f(x), dv = g'(x) dx

The Attempt at a Solution



I first started by pull the 9 out to the front:
9 integral of r4^r dr
I then set u=r, du=dr, dv=4^r, v=(4^r)/ln(4)
I used the formula: integral of udv = uv - integral vdu
and got: the integral of 9r4^r dr = [(r4^r)/ln4] - the inegral of (4^r)/ln4 dr
I then pulled the 1/ln4 out of the last part and got:
the integral of 9r4^r dr = [(r4^r)/ln4] - 1/ln4[the inegral of 4^r dr]

I was also able to get the anti-derivative of the [the inegral of 4^r dr] as (1/ln(4)) 4^r
I got stuck here, i don't know how to put all of it back together, help please?
 
Physics news on Phys.org
  • #2
You did all the hard stuff already, though you forgot to multiply the 9 through.

This is what you said you have so far:

[tex]\int 9r4^rdr=9\left(\frac{r4^r}{\log 4}-\frac{4^r}{(\log 4)^2}\right)[/tex]

Aren't you done except for tacking on +C to the end?
 
  • #3
yes, but does it needs to be simplified? how do you do that?
my assignment is online and it keeps on telling me that I'm getting the wrong answer.
 

FAQ: How do I Simplify This Integral: 9r4^r dr?

What does the notation "9r4^r dr" mean?

The notation "9r4^r dr" represents an integral, which is a mathematical concept used to describe the area under a curve. In this particular integral, "9" is the coefficient, "r" is the variable, "4" is the power, and "dr" indicates that the integral is being taken with respect to the variable "r".

How do I solve an integral like "9r4^r dr"?

To solve this integral, you can use the power rule of integration, which states that the integral of x^n is equal to x^(n+1)/(n+1). In this case, you can rewrite the integral as 9r^(4+1)/(4+1) = 9r^5/5 + C, where C is the constant of integration.

What is the purpose of solving an integral like "9r4^r dr"?

Solving an integral can help you find the area under a curve, which can be useful in many scientific and mathematical applications. It can also help you find the average value of a function over a given interval.

Can I use a calculator to solve an integral like "9r4^r dr"?

Yes, there are many online and offline calculators available that can help you solve integrals. However, it is important to understand the steps involved in solving an integral, as calculators may not always provide accurate results.

Are there any special techniques for solving an integral like "9r4^r dr"?

Yes, there are several integration techniques that can be used to solve different types of integrals. These include substitution, integration by parts, and trigonometric substitution. It is important to understand these techniques and when to apply them in order to solve integrals efficiently.

Similar threads

Back
Top